I guess google was broken for you?

Can most Android TVs run games like PSP emulators upscaled to 1080p and other play store games (like 3D Final Fantasy titles) at 30-60 framds?

Definitely not good emulation for anything beyond SNES era on a Nexus Player. The Nvidia Shield is a lot beefier, so it's possible, but I don't know.

Also, can you download apks from the internet onto these devices, such as Terrarium?

Yes. It's called sideloading. But apps not designed for TV may require a mouse and may not play well. Dunno about Terrarium.